12.0762
mol/L
440.3
g/L
12.0762
mol/L
440.3
g/L
Concentrated laboratory reagents — such as hydrochloric acid, sulfuric acid, nitric acid, ammonia, and hydrogen peroxide — are typically sold with their concentration expressed as a weight percent (% w/w) along with the solution density. To use these reagents in quantitative work, you need to convert this information into molarity (mol/L). This calculator performs that essential conversion using the formula: M = (% × d × 10) / Mw.
The factor of 10 arises from unit conversions: percent means grams per 100 grams of solution, density converts mass to volume (g/mL), and we need liters (1000 mL). The combined conversion factor is 1000/100 = 10. This is one of the most frequently performed calculations in analytical chemistry, especially when diluting concentrated stock solutions to prepare working standards.
Knowing the exact molarity of concentrated reagents is critical for accurate preparation of diluted solutions, stoichiometric calculations, and titration standardization. Common concentrated acids and their approximate molarities include: HCl (37%, 12.1 M), H₂SO₄ (98%, 18.4 M), HNO₃ (70%, 15.9 M), and H₃PO₄ (85%, 14.8 M).
The conversion formula relates percentage concentration, density, and molar mass to molarity:
M = (% × d × 10) / Mw
Where:
The derivation is straightforward: Consider 1 liter (1000 mL) of solution.
This calculator also outputs the mass concentration in g/L, computed as: C (g/L) = % × d × 10. This intermediate value is useful for verifying the calculation and for applications where mass concentration is preferred over molar concentration.
When using this formula, ensure the density corresponds to the same percentage concentration and temperature. Density values for common concentrated acids and bases are readily available in the CRC Handbook of Chemistry and Physics and on reagent bottle labels from suppliers like Sigma-Aldrich, Fisher Scientific, and Merck.
The calculated molarity tells you the exact molar concentration of the concentrated reagent. For example, 37% HCl with density 1.19 g/mL gives approximately 12.1 M. To prepare 1 L of 1 M HCl from this stock, you would need V = (1 × 1000) / 12.1 ≈ 82.6 mL of concentrated acid, diluted to 1 L with water (always add acid to water, never water to acid).
If your result differs significantly from known values for common reagents, double-check that the percentage is w/w (not w/v), the density units are g/mL, and the molar mass is correct.
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Standard concentrated HCl is 37% w/w with density 1.19 g/mL. This gives approximately 12.08 M, consistent with the commonly cited value of ~12 M on reagent labels.
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Concentrated H₂SO₄ at 98% w/w and density 1.84 g/mL has a molarity of approximately 18.4 M. This extremely concentrated solution requires extreme caution — always add acid to water slowly during dilution.
Check the label on the reagent bottle — manufacturers like Sigma-Aldrich, Fisher Scientific, and Merck always list the percentage (assay) and density (specific gravity). The Safety Data Sheet (SDS) also contains this information. For common acids and bases, reference values are available in the CRC Handbook of Chemistry and Physics.
The factor 10 comes from combining two unit conversions: percent means 'per 100' (dividing by 100) and liters to milliliters (multiplying by 1000). Combined: 1000/100 = 10. Without this factor, the formula would be M = (% / 100) × (d × 1000) / Mw, which simplifies to the same expression.
No, this formula is specifically for weight/weight percent (% w/w). For % w/v (grams per 100 mL), the formula is simpler: M = (% w/v × 10) / Mw. The density factor is not needed because % w/v already relates mass to volume.
Yes. Specific gravity is the ratio of the solution density to the density of water at 4°C (1.000 g/mL). Since the reference density is 1, specific gravity is numerically equal to density in g/mL for practical purposes. You can use the value directly in this formula.
Because the actual percentage and density vary slightly between production batches and manufacturers. The label on the bottle gives the actual assay percentage (e.g., 36-38% for HCl). For precise analytical work, you should standardize your solution by titrating against a primary standard rather than relying solely on the calculated molarity.
Always add acid to water, never water to acid (remember: 'Do as you oughta, add acid to water'). Adding water to concentrated acid can cause localized boiling and spattering due to the large exothermic heat of dilution. Calculate the required volume using C₁V₁ = C₂V₂, then slowly add the calculated volume of acid to a container of water while stirring. Allow to cool before adjusting to final volume.
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